Third-order boundary value problems with sign-changing solutions. (English) Zbl 1130.34010
The authors are concerned with the existence of sign-changing solutions for a third order differential equation
\[ u'''(t)=f(t,u(t),u'(t),u''(t)),\quad\text{ a.e. } t\in (0,1), \]
subject to the boundary conditions \(u(0)=u'(0)=u''(1)=0\) or \(u(0)=u'(1)=u''(1)=0\).
The proof of the main results are based on the Leray-Schauder continuation principle.
\[ u'''(t)=f(t,u(t),u'(t),u''(t)),\quad\text{ a.e. } t\in (0,1), \]
subject to the boundary conditions \(u(0)=u'(0)=u''(1)=0\) or \(u(0)=u'(1)=u''(1)=0\).
The proof of the main results are based on the Leray-Schauder continuation principle.
Reviewer: Ruyun Ma (Lanzhou)
MSC:
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
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